Pressure Dependence of Piezoelectric Field in InGaN/GaN Quantum Wells

Abstract

In this work we use the well width dependence of the quantum confined Stark effect to determine the variation of the built-in piezoelectric field in InGaN/GaN quantum wells with applied hydrostatic pressure. We find that the field increases from 1.4 MV/cm at atmospheric pressure to 2.6 MV/cm at 8.7 GPa. An analysis of the strain generated by the pressure suggests that the increase in the field is due to a dramatic dependence of the piezoelectric constants of GaN and InGaN on strain.Built-in piezoelectric fields (F pz ) play an important role in devices based on InGaN/ GaN quantum wells (QWs) with wurtzite lattice configuration. To quantify the effect of these fields one needs to know the exact geometry of the device, the strain state, and the piezoelectric constants of the materials forming the quantum wells. While the first two characteristics can be determined quite precisely, the latter one is subject to a significant uncertainty. The experimentally defined values of the piezoelectric constant e 33 of GaN range from 0.43 C/m 2 [1] to 1.12 C/m 2 [2], with the theoretically predicted values of 0.63-0.73 C/m 2 [3,4]. For InN the piezoelectric constants are not determined experimentally yet. The predicted value of e 33 in InN is 0.81 C/m 2 [5]. To even worsen this uncertainty, the piezoelectric constants of InGaN quantum wells are commonly linearly interpolated from the values of the piezoelectric constants of the binaries forming the alloy [6,7]. This approach neglects the effect of the microscopic strains associated with alloy mixing and the macroscopic strain generated by the lattice mismatch between GaN and InGaN. In this work we show that piezoelectric constants of GaN and InGaN have a dramatic dependence on the macroscopic strain. To reveal this dependence we apply hydrostatic pressure to the QW structures to modify the strain state in the wells and in the barriers. This results in a strikingly large increase of the F pz . An analysis of the strain state shows that the increase of the F pz arises from the nonlinear piezoelectric effect [3,8], i.e. the strain dependence of the piezoelectric constants.The QW structures studied in this work were grown by metal organic chemical vapour deposition on (0001) sapphire substrates. Each structure has four identical quantum wells with indium composition of~15% and GaN barriers. The barriers are 12.5 nm wide and the well widths in the three different samples are 2.5, 3.1, and 3.8 nm respectively. The QW regions are grown on 3.5 mm GaN layers.

Universal behavior of photoluminescence in GaN-based quantum wells under hydrostatic pressure governed by built-in electric field

“…4) agree very well with the experimental data when the effect of nonlinear piezoelectricity is included through changes in the first-order piezoelectric coefficients due to deviatoric strain. [28][29][30] …”

“…The role of the built-in electric field and its pressure increase in InGaN/GaN and GaN/AlGaN QWs has been confirmed by a significant rise of the PL decay-time with pressure. 28,29 The linear theory of elasticity and piezoelectricity was found insufficient to explain these results, and nonlinear piezoelectricity arising from strain dependence of the piezoelectric constants [28][29][30] together with nonlinear elasticity originating from pressure dependence of the elastic constants 16 were applied. However, accurate studies of the contributions of both nonlinear effects to the values of dE PL dP in nitride quantum structures have been limited by uncertainties in determining the composition dependence of dE G dP in nitride alloys.…”

“…We show that this experimental finding agrees with the numerical calculations performed in the framework of thek Áp method with excitonic effects, provided that the effects of nonlinear piezoelectricity and nonlinear elasticity are taken into account. The effect of nonlinear piezoelectricity is treated in two different ways, either by taking into account the strain dependence of the first-order piezoelectric constants, [28][29][30] or by including the second-order piezoelectric coefficients, which have recently been determined for nitride compounds in Ref. 31.…”

Pressure influence on bound polarons in a strained wurtzite GaN/AlxGa1−xN heterojunction under an electric field

“…( 5) where H e;i HS and H e;i IF stand for the Hamiltonians of the interactions between the electron and the HS and the IF phonons, respectively. It can be given as follows.…”

The Role of the Built-In Electric Field in Recombination Processes of GaN/AlGaN Quantum Wells: Temperature- and Pressure-Dependent Study of Polar and Non-Polar Structures

“…Non-polar systems are free from such negative features. Moreover, for polar QWs, the observed pressure coefficients of the PL energy (dE PL /dp) are reduced relative to those of the GaN energy gap [29][30][31][32][33][34][35][36][37][38][39][40][41]. This effect is caused by the hydrostatic-pressure-induced increase in the piezoelectric field in quantum structures [33][34][35]42].…”